# American Institute of Mathematical Sciences

2003, 2003(Special): 664-671. doi: 10.3934/proc.2003.2003.664

## Dynamics of principal configurations near umbilics for surfaces in $mathbb(R)^4$

 1 Facultad de Matemáticas, UADY, Calle 8 x 21 S/N, C.P. 97199, Mérida, Yuc., Mexico 2 Departamento de Matemáticas, Facultad de Ciencias, UNAM, Ciudad Universitaria, C.P. 04510, México, D.F., Mexico

Received  September 2002 Published  April 2003

The $v$-principal configuration of an immersed surface $M$ in $\mathbb(R)^4$ is the set formed by the umbilical points and the lines of principal curvatures with respect to an unitary smooth vector field $v$ normal to $M$. In this article we describe the bifurcation set of $v$-principal configurations of a local surface $M$ depending on two parameters of the surface and depending also on the 1-jet of the vector field $v$ normal to $M$ which defines an isolated simple umbilical point of $M$.
Citation: Matías Navarro, Federico Sánchez-Bringas. Dynamics of principal configurations near umbilics for surfaces in $mathbb(R)^4$. Conference Publications, 2003, 2003 (Special) : 664-671. doi: 10.3934/proc.2003.2003.664
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